Rigorous Numerics

  1. "Rigorous verification of bifurcations of differential equations via the Conley index theory"
     Kaname Matsue, SIAM Journal on Applied Dynamical Systems, 10 (2011), 325--359.
  2. "Rigorous numerics for stationary solutions of dissipative PDEs - Existence and local dynamics - "
     Kaname Matsue, NOLTA, 4 (2013), 62--79.
  3. "Rigorous numerics for fast-slow systems with one-dimensional slow variable: topological shadowing approach"
     Kaname Matsue, available on arXiv : 1507.01462, Topological Methods in Nonlinear Analysis (2017), doi=
     Validation data (entire note)
    fn_homoclinic : note, slow_manifold and shadowing (left), slow_manifold and shadowing (right), m-cone (left), m-cone (right), singular isolating block (left), singular isolating block (right)
  4. "On the construction of Lyapunov functions with computer assistance"
     Kaname Matsue, Tomohiro Hiwaki and Nobito Yamamoto, available on arXiv : 1604.05953, Journal of Computational and Applied Mathematics, 319(2017), 385-412
  5. "Numerical validation of blow-up solutions for ordinary differential equations"
     Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi and Shin'ichi Oishi, available on arXiv : 1606.03039, Journal of Computational and Applied Mathematics, 314(2017), 10-29, doi:10.1016/
  6. "Rigorous numerics of tubular, conic, star-shaped neighborhoods of slow manifolds for fast-slow systems"
     Kaname Matsue, available on arXiv : 1612.02162
  7. "Numerical validation of blow-up solutions with quasi-homogeneous compactifications"
     Kaname Matsue and Akitoshi Takayasu, available on arXiv : 1707.05936

Dynamical Systems

  1. "On blow-up solutions of differential equations with Poincare-type compactifications"
     Kaname Matsue, available on arXiv : 1611.06346
  2. "Toward a mathematical analysis for a model of suspension flowing down an inclined plane"
     Kaname Matsue and Kyoko Tomoeda, available on arXiv : 1709.00409, submitted.

Topology Optimization

  1. "二値の熱伝導率を持つ領域の第一固有値に対する最適配置"
     松江 要, 内藤 久資, 応用数理, 23 (no.4, 2013), 10--15.
  2. "Numerical studies of the optimization of the first eigenvalue of the heat diffusion in inhomogeneous media"
     Kaname Matsue, Hisashi Naito, available on arXiv : 1408.5370, Japan Journal of Industrial and Applied Mathematics, 32(2015), 489--512, doi:10.1007/s13160-015-0177-5
  3. "非一様拡散係数を持つ熱方程式固有値問題の第一固有値の最適化 -粘性近似問題の大域適切性-"
     松江 要, 内藤 久資, RIMS Kokyuroku Bessatsu, B54-3(2016), 25--48.

Materials Science

  1. "Geometric frustration of icosahedron in metallic glasses"
     Akihiko Hirata, L.J. Kang, Takeshi Fujita, B. Klumov, Kaname Matsue, Motoko Kotani, A.R. Yavari and MingWei Chen, Science, 341 (2013), 376--379, DOI: 10.1126/science.1232450.
  2. (No reviewed proceedings) "計算ホモロジーによるガラスの特徴付け"
     松江 要, 平田 秋彦, 数理解析研究所講究録 2005(2016), 97--107
  3. "Hierarchical structures of amorphous solids characterized by persistent homology"
     Yasuaki Hiraoka, Takenobu Nakamura, Akihiko Hirata, Emerson G. Escolar, Kaname Matsue and Yasumasa Nishiura, available on arXiv : 1501.03611, Proceedings of the National Academy of Sciences of the United States of America, 113(2016), 7035--7040, doi: 10.1073/pnas.1520877113
  4. (Monograph) "Structural analysis of metallic glasses with computational homology"
     Akihiko Hirata, Kaname Matsue and MingWei Chen, "Springer Briefs in Mathematics of Materials", ISBN (online) : 978-4-431-56056-2

Quantum Walks

  1. "Quantum walks on simplicial complexes"
     Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, available on arXiv : 1507.01194, Quantum Information Processing, 15(2016), 1865--1896, doi:10.1007/s11128-016-1247-6
  2. (No reviewed proceedings) "量子ウォーク - ダイナミクスと幾何構造 -"
     松江 要, 小栗栖 修, 瀬川 悦生, 数理解析研究所講究録 1986(2016), 37--54
  3. "A note on the spectral mapping theorem of quantum walk models"
     Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, available on arXiv : 1604.00581, Interdisciplinary Information Science, 23(2017), 105--114.
  4. "Quaternionic quantum walks of Szegedy type and zeta functions of graphs",
     Norio Konno, Kaname Matsue, Hideo Mitsuhashi and Iwao Sato, arXiv:1703.04969
  5. "Quantum search on simplicial complexes",
     Kaname Matsue, Osamu Ogurisu and Etsuo Segawa, arXiv:1707.00156, Quantum Studies: Mathematics and Foundations,
  6. "Resonant-tunneling in discrete-time quantum walk",
     Kaname Matsue, Leo Matsuoka, Osamu Ogurisu and Etsuo Segawa, arXiv:1708.01052

In Preparation

  1. "Topological shadowing and rigorous numerics for fast-slow systems with multi-dimensional slow variables"
     Kaname Matsue, in preparation.
  2. "Geometric treatments of blow-up solutions for ODEs"
     Kaname Matsue, in preparation.
  3. (Something new.)
     Kaname Matsue, in preparation.

Abstracts (in reverse chronological order)





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